Need advice on turning a 2D image into a 3D model
I started off by adding the image you posted as a material texture on a plane that was UV un-wrapped using the default option that shows up at the top of the list which is called Unwrap. 

Then I unchecked the Color channel for this texture and used the Normal Channel instead.  Sometimes when adding a color or greyscale texture as a bump map will cause the effect to look inverted so if this happens then you can use a value of -1.0 instead of 1.0

The image at the left is the Tangent map I baked that captures the bump map as surface normals.


There was some noise in the baked image so I saved it and opened it with GIMP and blurred the tangent map using Gaussian Blur set to 10 pixels.  Now I reloaded this tangent map into Blender and replaced the image that you posted and changed the Mapping Type to Normal Map-> Tangent.  I also changed the -1.0 to +1.0 for the Normal value.

Here is now what it looks like after the blur.  



For simple planes like this, it's fine to blur the normal map but for complex objects this will not work well since the seams will become immediately obvious even for a very subtle blur.  

One thing I forgot to mention is that normal maps that are saved as .png are in sRGB format and if you plan to use Cycles then they should be set to non-color format.  It doesn't seem to matter for Blender Internal View-port drawing.